Show simple item record

dc.contributor.authorBai, Shuyangen_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.date.accessioned2019-08-22T20:46:09Z
dc.date.available2019-08-22T20:46:09Z
dc.date.issued2017-02-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000389565500027&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationShuyang Bai, Murad S Taqqu. 2017. "The impact of the diagonals of polynomial forms on limit theorems with long memory." BERNOULLI, Volume 23, Issue 1, pp. 710 - 742 (33). https://doi.org/10.3150/15-BEJ697
dc.identifier.issn1350-7265
dc.identifier.issn1573-9759
dc.identifier.urihttps://hdl.handle.net/2144/37218
dc.description.abstractWe start with an i.i.d. sequence and consider the product of two polynomial-forms moving averages based on that sequence. The coefficients of the polynomial forms are asymptotically slowly decaying homogeneous functions so that these processes have long memory. The product of these two polynomial forms is a stationary nonlinear process. Our goal is to obtain limit theorems for the normalized sums of this product process in three cases: exclusion of the diagonal terms of the polynomial form, inclusion, or the mixed case (one polynomial form excludes the diagonals while the other one includes them). In any one of these cases, if the product has long memory, then the limits are given by Wiener chaos. But the limits in each of the cases are quite different. If the diagonals are excluded, then the limit is expressed as in the product formula of two Wiener–Itô integrals. When the diagonals are included, the limit stochastic integrals are typically due to a single factor of the product, namely the one with the strongest memory. In the mixed case, the limit stochastic integral is due to the polynomial form without the diagonals irrespective of the strength of the memory.en_US
dc.description.sponsorshipWe would like to thank an anonymous referee for careful reading and constructive suggestions. This work was partially supported by the NSF Grants DMS-10-07616 and DMS-13-09009 at Boston University. (DMS-10-07616 - NSF at Boston University; DMS-13-09009 - NSF at Boston University)en_US
dc.format.extent710 - 742 (33)en_US
dc.languageEnglish
dc.publisherINT STATISTICAL INSTen_US
dc.relation.ispartofBERNOULLI
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectDiagonalsen_US
dc.subjectLong memoryen_US
dc.subjectNoncentral limit theoremen_US
dc.subjectSelf-similar processesen_US
dc.subjectVolterraen_US
dc.subjectWieneren_US
dc.subjectStatisticsen_US
dc.subjectEconometricsen_US
dc.titleThe impact of the diagonals of polynomial forms on limit theorems with long memoryen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.3150/15-BEJ697
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-1145-9082 (Taqqu, Murad S)
dc.identifier.mycv54238


This item appears in the following Collection(s)

Show simple item record